I have similar reading interests. There is an astonishing number of original accounts from that time. Your question specified books about hunting and lifestyle. One you don't see mentioned much is Wild Sports in the Far West, by Frederick Gerstaecker. This is not a "mountain man" book, but was written by a young German sportsman without a lot of money who traveled to the US in the late 1830's. Most of his adventures took place in Arkansas. He hunted bear, turkeys, deer, and even alligators. He lived with the pioneer families, and befriended and hunted with Indians, mostly from the eastern tribes that had been "removed" to the Indian Territory. Gerstaecker was a very keen hunter, and a good writer. He described hunting techniques in detail. He was fascinated by the people of the frontier, also, and he wrote extensively about them and life on the frontier. He was not a wealthy duke with a retinue of servants, either... He had to work to support himself the whole time. I would not pass this one up because it isn't specifically about mountain men, and it is definitely from that era. Google the title, and scroll through the "hits" until you find the one for Google Books. The entire volume is online, and you can read it for free.
Another one is Solitary Rambles, by John Palliser. Again, Google the author and title and you will find a digitized copy online. I don't recall the date of Palliser's time in the US... I'm thinking the 1850's, but will need to check. He was Irish, and came to the northern plains specifically to hunt. This book is all about his hunting exploits. He stayed at several of the frontier trading "forts," and met a number of trappers and plainsmen. The fur trade did not stop in 1840. It's just that the rendezvous system was made obsolete by the construction of more trading facilities in the west, and with the decline in both supply and demand for beaver, the trade became more diversified. Wolf skins, for example, were highly valued, and the buffalo robe trade was in full swing. Palliser was also a "gun nut," and he wrote a great deal about his weapons and gear.
Those two ought to get you going. There are dozens of great books out there. I have read a lot of them, but keep finding more titles that are totally new to me.
Best of luck to you,
Notchy Bob
